The rapid adoption of AI in Earth system science promises unprecedented speed and fidelity in the generation of climate information. However, this technological prowess rests on a fragile and unequal foundation: the current trajectory of AI development risks further automating and amplifying the North-South divide in the global climate information system. We outline the global asymmetry in High-Performance Computing and data infrastructure, demonstrating that the development of foundation models is almost exclusively concentrated in the Global North. Using three different domains, we show how this infrastructure inequality continues through models' inputs, processes and outputs. As an example, in weather and climate modelling, the reliance on historically biased data leads to systematic performance gaps that disproportionately affect the most vulnerable regions. In climate impact modelling, data sparsity and unrepresentative validation risk driving misleading interventions and maladaptation. Finally, in large language models, dependence on dominant textualised forms of climate knowledge risks reinforcing existing biases. We conclude that addressing these disparities demands revisiting the three phases, i.e. models Input, Process and Output. This involves (i) a perspective shift from model-centric to data-centric development, (ii) the establishment of a Climate Digital Public Infrastructure and human-centric evaluation metrics, and (iii) a move from producer-consumer dynamics toward knowledge co-production. This integration of diverse knowledge systems would truly democratise compute sovereignty and ensure that the AI revolution fosters genuine systemic resilience rather than exacerbating inequity.